Proving this seems difficult at first, but Cantor’s reasoning was so simple and original that it is worth understanding it. His is a ‘proof by contradiction’. Here we start with a statement that is opposite of what we want to prove and then show that this leads to an inconsistency.

- Let us take the entire set of decimal numbers i.e.
*all*the numbers between [0,1]. This means that the rational and irrational numbers are in this together. And we know that the fractions or the rational numbers are ‘countably infinite’.

*The essence of Cantor’s proof is that we assume that the decimals* (irrational & rational numbers both put together) *are as numerous as the natural numbers* ( i.e. integers, and we have shown above that the rational numbers have the same infinity** א _{0}**, as the integers themselves)

Let us accordingly number the list a_{1}, a_{2}, a_{3}, a_{4} and so on :-

We imagine each a_{1}, a_{2}, a_{3} etc. to be a decimal number that continues indefinitely. In case it terminates (i.e. it is rational and is an exact fraction) then we will fill up the digits with zeros.

■■ A single letter of the alphabet in Sanskrit is called akshara. In the Upanishads Brahman, the Unknown is also called akshara.[13] For, akshara has neither any substance nor...

Now Chāndogya Upaniśad IV.10.5 establishes the duality of Brahman, the Unknown’s desire to be by saying that….. Here Agnī Deva, the Lord of Energy is explaining the secret...